Top and bottom placeholders are the only placeholders available as of now.
Secondly, the rendering of items in the Gear menu is controlled by Microsoft. So, in SharePoint online, its not recommended to customise it because changes pushed by Microsoft might overwrite your customisation.
So, what i would recommend is that you insert a button in the top placeholder and then on the click of it, show the metadata of the site by making an AJAX request. The permission checking for a group of people can be done via REST calls. That way, you will be able to control the visibility of the button.